Regularisation methods for imaging from electrical measurements

In Electrical Impedance Tomography the conductivity of an object is estimated from boundary measurements. An array of electrodes is attached to the surface of the object and current stimuli are applied via these electrodes. The resulting voltages are measured. The process of estimating the conductivity as a function of space inside the object from voltage measurements at the surface is called reconstruction. Mathematically the ElT reconstruction is a non linear inverse problem, the stable solution of which requires regularisation methods. Most common regularisation methods impose that the reconstructed image should be smooth. Such methods confer stability to the reconstruction process, but limit the capability of describing sharp variations in the sought parameter. In this thesis two new methods of regularisation are proposed. The first method, Gallssian anisotropic regularisation, enhances the reconstruction of sharp conductivity changes occurring at the interface between a contrasting object and the background. As such changes are step changes, reconstruction with traditional smoothing regularisation techniques is unsatisfactory. The Gaussian anisotropic filtering works by incorporating prior structural information. The approximate knowledge of the shapes of contrasts allows us to relax the smoothness in the direction normal to the expected boundary. The construction of Gaussian regularisation filters that express such directional properties on the basis of the structural information is discussed, and the results of numerical experiments are analysed. The method gives good results when the actual conductivity distribution is in accordance with the prior information. When the conductivity distribution violates the prior information the method is still capable of properly locating the regions of contrast. The second part of the thesis is concerned with regularisation via the total variation functional. This functional allows the reconstruction of discontinuous parameters. The properties of the functional are briefly introduced, and an application in inverse problems in image denoising is shown. As the functional is non-differentiable, numerical difficulties are encountered in its use. The aim is therefore to propose an efficient numerical implementation for application in ElT. Several well known optimisation methods arc analysed, as possible candidates, by theoretical considerations and by numerical experiments. Such methods are shown to be inefficient. The application of recent optimisation methods called primal- dual interior point methods is analysed be theoretical considerations and by numerical experiments, and an efficient and stable algorithm is developed. Numerical experiments demonstrate the capability of the algorithm in reconstructing sharp conductivity profiles

Grid sensitivity for aerodynamic optimization and flow analysis

After reviewing relevant literature, it is apparent that one aspect of aerodynamic sensitivity analysis, namely grid sensitivity, has not been investigated extensively. The grid sensitivity algorithms in most of these studies are based on structural design models. Such models, although sufficient for preliminary or conceptional design, are not acceptable for detailed design analysis. Careless grid sensitivity evaluations, would introduce gradient errors within the sensitivity module, therefore, infecting the overall optimization process. Development of an efficient and reliable grid sensitivity module with special emphasis on aerodynamic applications appear essential. The organization of this study is as follows. The physical and geometric representations of a typical model are derived in chapter 2. The grid generation algorithm and boundary grid distribution are developed in chapter 3. Chapter 4 discusses the theoretical formulation and aerodynamic sensitivity equation. The method of solution is provided in chapter 5. The results are presented and discussed in chapter 6. Finally, some concluding remarks are provided in chapter 7

The accurate numerical inversion of laplace transforms

Inversion of almost arbitrary Laplace transforms is effected by trapezoidal integration along a special contour. The number n of points to be used is one of several parameters, in most cases yielding absolute errors of order 10-7 for n = 10, 10-11 for n = 20, 10-23 for n = 40 (with double precision working), and so on, for all values of the argument from 0+ up to some large maximum. The extreme accuracy of which the method is capable means that it has many possible applications of various kinds, and some of these are indicated

Wavelet-based semiconductor device simulation.

by Pun Kong-Pang.Thesis (M.Phil.)--Chinese University of Hong Kong, 1997.Includes bibliographical references (leaves 94-[96]).Acknowledgement --- p.iAbstract --- p.iiiList of Tables --- p.viiList of Figures --- p.viiiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Role of Device Simulation --- p.2Chapter 1.2 --- Classification of Device Models --- p.3Chapter 1.3 --- Sections of a Typical Simulator --- p.6Chapter 1.4 --- Arrangement of This Thesis --- p.7Chapter 2 --- Classical Physical Model --- p.9Chapter 2.1 --- Carrier Densities --- p.12Chapter 2.2 --- Space Charge --- p.14Chapter 2.3 --- Carrier Mobilities --- p.15Chapter 2.4 --- Generation and Recombination --- p.17Chapter 2.5 --- Modeling of Device Boundaries --- p.20Chapter 2.6 --- Limits of Classical Device Modeling --- p.22Chapter 3 --- Computational Aspects --- p.23Chapter 3.1 --- Normalization --- p.24Chapter 3.2 --- Discretization --- p.26Chapter 3.2.1 --- Finite Difference Method --- p.26Chapter 3.2.2 --- Finite Element Method --- p.27Chapter 3.3 --- Nonlinear Systems --- p.28Chapter 3.3.1 --- Newton's Method --- p.28Chapter 3.3.2 --- Gummel's Method and its modification --- p.29Chapter 3.3.3 --- Comparison and discussion --- p.30Chapter 3.4 --- Linear System and Sparse Matrix --- p.32Chapter 4 --- Cubic Spline Wavelet Collocation Method for PDEs --- p.34Chapter 4.1 --- Cubic spline scaling functions and wavelets --- p.35Chapter 4.1.1 --- Approximation for a function in H2(I) --- p.43Chapter 4.2 --- Wavelet interpolation --- p.45Chapter 4.2.1 --- Interpolant operator Ivo in Vo --- p.45Chapter 4.2.2 --- Interpolation operator IWjf in Wj --- p.47Chapter 4.3 --- Derivative Matrices --- p.51Chapter 4.3.1 --- First derivative matrix --- p.51Chapter 4.3.2 --- Second derivative matrix --- p.53Chapter 4.4 --- Wavelet Collocation Method for Solving Device Equations --- p.55Chapter 4.4.1 --- Steady state solution --- p.57Chapter 4.4.2 --- Transient solution --- p.58Chapter 4.5 --- Reducing Collocation Points --- p.59Chapter 4.5.1 --- Error evaluation --- p.59Chapter 4.5.2 --- Deleting collocation points --- p.61Chapter 5 --- Numerical Results --- p.64Chapter 5.1 --- P-N Junction Diode --- p.64Chapter 5.1.1 --- Steady state solution --- p.69Chapter 5.1.2 --- Transient solution --- p.76Chapter 5.1.3 --- Convergence --- p.79Chapter 5.2 --- Bipolar Transistor --- p.81Chapter 5.2.1 --- Boundary Model --- p.82Chapter 5.2.2 --- DC Solution --- p.83Chapter 5.2.3 --- Transient Solution --- p.89Chapter 6 --- Conclusions --- p.92Bibliography --- p.9

PROTEUS two-dimensional Navier-Stokes computer code, version 1.0. Volume 3: Programmer's reference

A new computer code was developed to solve the 2-D or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The thin-layer or Euler equations may also be solved. Turbulence is modeled using an algebraic eddy viscosity model. The objective was to develop a code for aerospace applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The equations are written in nonorthogonal body-fitted coordinates, and solved by marching in time using a fully-coupled alternating-direction-implicit procedure with generalized first- or second-order time differencing. All terms are linearized using second-order Taylor series. The boundary conditions are treated implicitly, and may be steady, unsteady, or spatially periodic. Simple Cartesian or polar grids may be generated internally by the program. More complex geometries require an externally generated computational coordinate system. The documentation is divided into three volumes. Volume 3 is the Programmer's Reference, and describes the program structure, the FORTRAN variables stored in common blocks, and the details of each subprogram

Solutions of linear equations and a class of nonlinear equations using recurrent neural networks

Artificial neural networks are computational paradigms which are inspired by biological neural networks (the human brain). Recurrent neural networks (RNNs) are characterized by neuron connections which include feedback paths. This dissertation uses the dynamics of RNN architectures for solving linear and certain nonlinear equations. Neural network with linear dynamics (variants of the well-known Hopfield network) are used to solve systems of linear equations, where the network structure is adapted to match properties of the linear system in question. Nonlinear equations inturn are solved using the dynamics of nonlinear RNNs, which are based on feedforward multilayer perceptrons. Neural networks are well-suited for implementation on special parallel hardware, due to their intrinsic parallelism. The RNNs developed here are implemented on a neural network processor (NNP) designed specifically for fast neural type processing, and are applied to the inverse kinematics problem in robotics, demonstrating their superior performance over alternative approaches

Observers for discrete-time nonlinear systems

Observer synthesis for discrete-time nonlinear systems with special applications to parameter estimation is analyzed. Two new types of observers are developed. The first new observer is an adaptation of the Friedland continuous-time parameter estimator to discrete-time systems. The second observer is an adaptation of the continuous-time Gauthier observer to discrete-time systems. By adapting these observers to discrete-time continuous-time parameter estimation problems which were formerly intractable become tractable. In addition to the two newly developed observers, two observers already described in the literature are analyzed and deficiencies with respect to noise rejection are demonstrated. improved versions of these observers are proposed and their performance demonstrated. The issues of discrete-time observability, discrete-time system inversion, and optimal probing are also addressed